What are the derivatives of the inverse trigonometric functions? How do the domains of the derivatives compare with the domains of the functions?

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What are the derivatives of the inverse trigonometric functions?    How do the domains of the derivatives compare with the domains of the functions?

Elberte · Accepted Answer

Step 1 To find the derivatives of inverse trignometric function and compare the domain of the function with the domain of the derivatives. Step 2 Derivatives of inverse Trignometric functions: (sin−1x)=11−x2 (cos−1x)=−11−x2 (tan−1x)=11+x2 (cot−1x)=−11+x2 (sec−1x)=1|x|x2−1 (cos⁡ec−1x)=−1|x|x2−1 Step 3 Domain of the derivatives of inverse Trignometric functions: KFunctionDomian(sin−1⁡x)‘−1&amp;lt;x&amp;lt;1(cos−1⁡x)‘−1&amp;lt;x&amp;lt;1(tan−1⁡x)‘−∝&amp;lt;x&amp;lt;∝(cot−1⁡x)‘−∝&amp;lt;x&amp;lt;∝(sec−1⁡x)‘x∈(−∝,−1)∪(1,∝)(cos⁡ec−1x)‘x∈(−∝,−1)∪(1,∝) Step 4 Domain of Inverse Trignometric Functions: FunctionDomian(sin−1⁡x)‘−1≤x≤1(cos−1⁡x)‘−1≤x≤1(tan−1⁡x)‘−∝&amp;lt;x&amp;lt;∝(cot−1⁡x)‘−∝&amp;lt;x&amp;lt;∝(sec−1⁡x)‘x∈(−∝,−1]∪[1,∝)(cos⁡ec−1x)‘x∈(−∝,−1]∪[1,∝) As we can conclude from the above tables that the domains of the derivatives of inverse trignometric, functions are restrictive appropriately.

What are the derivatives of the inverse trigonometric functions? How do th

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